HDU5130 Signal Interference

 /*
  HDU5130 Signal Interference
  http://acm.hdu.edu.cn/showproblem.php?pid=5130
  计算几何 圆与多边形面积交
  *
  */

 #include <cstdio>
 #include <algorithm>
 #include <cmath>
 using namespace std;
 const double Pi=acos(-1.0);
 const double eps = 1e-;
 const int Nmax=;
 double k;
 int sgn(double x)
 {
     if(x<-eps)
         return -;
     if(x>eps)
         return ;
     return ;
 }
 double Abs(double x)
 {
     if(sgn(x)<)
         x=-x;
     else if(sgn(x)==)
         x=0.0;
     return x;
 }
 double sqr(double x)
 {
     return x*x;
 }
 double Sqrt(double x)
 {
     return max(0.0,sqrt(x));
 }
 struct Pt
 {
     double x,y;
     Pt() { }
     Pt(double x, double y) : x(x), y(y) { }

     Pt operator - (const Pt &b)
     {
         return Pt(x-b.x,y-b.y);
     }
     Pt operator + (const Pt &b)
     {
         return Pt(x+b.x,y+b.y);
     }
     friend Pt operator * (double a,Pt p)
     {
         return Pt(p.x*a,p.y*a);
     }
     friend Pt operator * (Pt p,double a)
     {
         return Pt(p.x*a,p.y*a);
     }
     friend Pt operator / (Pt p,double a)
     {
         return Pt(p.x/a,p.y/a);
     }
     double norm()
     {
         return Sqrt(x*x + y*y);
     }
     double len()
     {
         return norm();
     }
     void print()
     {
         printf("(%f, %f)\n", x, y);
     }
 };
 int n;
 Pt pl[Nmax];
 Pt pr,A,B,p0,p1;
 double dist (Pt a, Pt b)
 {
     return (a-b).norm();
 }
 double dot(Pt a,Pt b)//点乘
 {
     return a.x*b.x+a.y*b.y;
 }
 double det(Pt a,Pt b)
 {
     return a.x*b.y-a.y*b.x;
 }
 Pt rotate(Pt p,double a)//P点绕原点逆时针旋转a弧度
 {
     return Pt(p.x*cos(a)-p.y*sin(a),p.x*sin(a)+p.y*cos(a));
 }
 struct Sg//线段
 {
     Pt s, t;
     Sg() { }
     Sg(Pt s, Pt t) : s(s), t(t) { }
     Sg(double a, double b, double c, double d) : s(a, b), t(c, d) { }
 };
 bool PtOnSegment(Pt p, Pt a, Pt b) //p是否在线段ab上，把<=改成<就能实现不含线段端点的点在线段上的判断。
 {
     return !sgn(det(p-a, b-a)) && sgn(dot(p-a, p-b)) <= ;
 }
 bool PtOnLine(Pt p, Pt a, Pt b) //p是否在直线ab上
 {
     return !sgn(det(p-a, b-a));
 }
 Pt PtLineProj(Pt s, Pt t, Pt p) //p到直线st的投影
 {
     double r = dot(p-s, t-s) / (t - s).norm();
     return s + (t - s) * r;
 }
 bool parallel(Pt a, Pt b, Pt s, Pt t)
 {
     return !sgn(det(a-b, s-t));
 }
 Pt triangleMassCenter(Pt a, Pt b, Pt c)
 {
     return (a+b+c) / 3.0;
 }
 double polygon_area(Pt poly[],int n)
 {
     double ans=0.0;
     if(n<)
         return ans;
     for(int i=;i<=n;i++)
         ans+=det(poly[i],poly[i%n+]);
     return ans*0.5;
 }

 struct Circle
 {
     Pt c;
     double r;
     Circle(Pt _c,double _r)
     {
         c=_c;
         r=_r;
     }
 };
 bool PointInCircle(Circle a,Pt p)
 {
     Pt c=a.c;
     return sgn( (p-c).norm()-a.r )<;
 }

 bool PointOnCircle(Circle a,Pt p)
 {
     Pt c=a.c;
     return sgn( (p-c).norm()-a.r )==;
 }

 bool PointIOCircle(Circle a,Pt p)
 {
     Pt c=a.c;
     return sgn( (p-c).norm()-a.r )<=;
 }

 void circle_cross_line(Circle c,Pt a, Pt b, Pt ans[], int &num)
 {
     double x1=a.x,y1=a.y,x2=b.x,y2=b.y;
     double dx=x2-x1,dy=y2-y1;
     double tmpx=x1-c.c.x,tmpy=y1-c.c.y;
     double A=dx*dx+dy*dy;
     double B=2.0*( dx*tmpx+dy*tmpy );
     double C=tmpx*tmpx+tmpy*tmpy-c.r*c.r;
     double delta=B*B-4.0*A*C;
     num=;
     if(sgn(delta)<)
         return;
     double t1=(-B-Sqrt(delta))/(2.0*A);
     double t2=(-B+Sqrt(delta))/(2.0*A);
     if(sgn(t1-1.0)<= && sgn(t1)>=)
         ans[++num]=Pt(x1+t1*dx,y1+t1*dy);
     if(sgn(delta)==)
         return;
     if(sgn(t2-1.0)<= && sgn(t2)>=)
         ans[++num]=Pt(x1+t2*dx,y1+t2*dy);
 }   

 double sector_area(Circle c,Pt a,Pt b)
 {
     a=a-c.c,b=b-c.c;
     double theta = atan2(a.y, a.x) - atan2(b.y, b.x);
     while (sgn(theta) <= ) theta += 2.0*Pi;
     while (sgn(theta-2.0*Pi)>) theta -= 2.0*Pi;
     theta = min(theta, 2.0*Pi - theta);
     return c.r*c.r*theta*0.5;
 }

 double CirclePolyArea(Circle c,Pt poly[],int n)
 {
     double ans=0.0;
     Pt p[];
     int num;
     for(int i=;i<=n;i++)
     {
         Pt a=poly[i],b=poly[i%n+];
         int ina=PointInCircle(c,a);
         int inb=PointInCircle(c,b);
         Pt da=a-c.c,db=b-c.c;
         int s=sgn(det(da,db));
         double part=0.0;
         if(ina)
         {
             if(inb)
             {
                 part=Abs(det(da,db))*0.5;
             }
             else
             {
                 circle_cross_line(c,a,b,p,num);
                 part=sector_area(c,p[],b)+Abs(det(da,p[]-c.c))*0.5;
             }
         }
         else
         {
             if(inb)
             {
                 circle_cross_line(c,a,b,p,num);
                 part=sector_area(c,p[],a)+Abs(det(db,p[]-c.c))*0.5;
             }
             else
             {
                 circle_cross_line(c,a,b,p,num);
                 if(num==)
                 {
                     part=sector_area(c,a,p[])+sector_area(c,b,p[])+Abs(det(p[]-c.c,p[]-c.c))*0.5;
                 }
                 else
                 {
                     part=sector_area(c,a,b);
                 }
             }
         }
         if(s!=)
             ans+=1.0*s*part;
     }
     return ans;
 }
 int main()
 {
    int t=;
     while(scanf("%d%lf",&n,&k)==)
     {
         t++;
         for(int i=;i<=n;i++)
             scanf("%lf%lf",&pl[i].x,&pl[i].y);
         scanf("%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y);
         double r;
         double E=(2.0*B.x-2.0*sqr(k)*A.x)/(1.0-sqr(k));
         double F=(2.0*B.y-2.0*sqr(k)*A.y)/(1.0-sqr(k));
         double G=(sqr(k*A.x)+sqr(k*A.y)-sqr(B.x)-sqr(B.y))/(1.0-sqr(k));
         pr.x=E/2.0,pr.y=F/2.0;
         r=Sqrt(G+sqr(E)/4.0+sqr(F)/4.0);
         Circle C(pr,r);
         double ans=Abs( CirclePolyArea(C,pl,n) );
         printf("Case %d: ",t);
         printf("%.10f\n",ans+eps);
     }
     return ;
 }